Related papers: Nearly optimal quantum algorithm for generating th…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
Gaussian states hold a fundamental place in quantum mechanics, quantum information, and quantum computing. Many subfields, including quantum simulation of continuous-variable systems, quantum chemistry, and quantum machine learning, rely on…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
We present a novel quantum algorithm for approximating the ground-state in quantum many-body systems, particularly suited for Noisy Intermediate-Scale Quantum (NISQ) devices. Our approach integrates Variational Quantum Eigensolvers (VQE)…
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the…
The initialization of quantum states or Quantum State Preparation (QSP) is a basic subroutine in quantum algorithms. In the worst case, general QSP algorithms are expensive due to the application of multi-controlled gates required to build…
We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon…
Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…
Finding the ground state of complex quantum systems remains a central challenge in many-body physics, quantum chemistry, and combinatorial optimization, due to the exponential growth of the Hilbert-space dimension and the entangled…
It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an…
We investigate Riemannian gradient flows for preparing ground states of a desired Hamiltonian on a quantum device. We show that the number of steps of the corresponding Riemannian gradient descent (RGD) algorithm that prepares a ground…
Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum…
Classical diffusion models have shown superior generative results. Exploring them in the quantum domain can advance the field of quantum generative learning. This work introduces Quantum Generative Diffusion Model (QGDM) as their simple and…
We study the approximate state preparation problem on noisy intermediate-scale quantum (NISQ) computers by applying a genetic algorithm to generate quantum circuits for state preparation. The algorithm can account for the specific…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…
Computing vacuum states of lattice gauge theories (LGTs) containing fermionic degrees of freedom can present significant challenges for classical computation using Monte-Carlo methods. Quantum algorithms may offer a pathway towards more…